A linear amplification with nonlinear components (LINC) modulator is provided. The LINC modulator includes: a separator that generates a plurality of constant envelope signals from a source signal; a processor that receives an input signal and detects and removes a phase jump in phase trajectory of the input signal to generate a first signal having a continuous phase trajectory and a second signal having a discontinuous phase trajectory; and a quadrature modulator that mixes the first signal with the second signal to reconstruct the input signal.